Compressed quantum metrology for the Ising Hamiltonian
arXiv:1608.02620 · doi:10.1103/PhysRevA.94.062326
Abstract
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling, i.e., O(1/N^2) precision and derive the explicit circuit that accomplishes the simulation.
arXiv comment11 pages, 4 figures
References in corpus (23)
- Elementary gates for quantum computation
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- On the Improvement of Frequency Stardards with Quantum Entanglement
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Ground state overlap and quantum phase transitions
- The elusive Heisenberg limit in quantum enhanced metrology
- Quantum limits in optical interferometry
- Quantum criticality as a resource for quantum estimation
- Classical simulation of noninteracting-fermion quantum circuits
- Matchgates and classical simulation of quantum circuits
- Quantum metrology for a general Hamiltonian parameter
- Quantum circuits for strongly correlated quantum systems
- Optimal quantum estimation in spin systems at criticality
- Efficient tools for quantum metrology with uncorrelated noise
- Phase transitions in an Ising chain interacting with a single mode cavity field
- Quantum metrology for the Ising Hamiltonian with transverse magnetic field
- Matchgate and space-bounded quantum computations are equivalent
- Achieving sub-shot-noise sensing at finite temperatures
- Compressed quantum simulation of the Ising model
- Adiabatic Time Evolution in Spin-Systems
- Compressed Simulation of evolutions of the XY-model
- Compressed simulation of thermal and excited states of the 1-D XY-model
Cited by in corpus (7)
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
- Compressed quantum computation using the IBM Quantum Experience
- Fidelity susceptibility in Gaussian Random Ensembles
- Integrable quantum many-body sensors for AC field sensing
- Quantum-enhanced sensing with variable-range interactions
- Precision magnetometry exploiting excited state quantum phase transitions